Could someone help me with the following?
A function f on R to R satisfies for all x,y
abs(f(x)-f(y)) less than or equal to k*abs(x-y) where k is a constant greater than zero.
First, prove that f is continuous. Also, use this to show that given an epsilon greater than 0, there is at least one delta greater than zero that "measures" the continuity for this epsilon at all points.
Thanks a lot. I have no idea what I'm doing.